Space Grant Consortium - University of Wisconsin - Green Bay

UA
m�
⎛ ε −1
⎞
( c nd c st MR
2 , pc, i 1 , pc, i ) ⎜ ⎟ ( Crpci
, , )
pc, i pc, i
2
nd
= min , ln −1
⎜εC−1⎟ ⎝ pc, i r, pc, i ⎠
where Cr,pc,i is the capacity ratio characterizing the section:
( nd st ) ( nd st )
rpci , , 2 , pc, i 1 , pc, i 2 , pc, i 1 , pc, i
i = 1… Npc (21)
C = min c , c MR max c , c MR i = 1… Npc (22)
The overall conductance of the precooler per unit of 2 nd stage mass flow rate is computed by
summing the conductances of each of the segments.
UA N
pc UApc,
i
= ∑
i = 1... Npc (23)
m� m�
2 i=
1 2
nd nd
2 nd Stage Analysis. The thermodynamic states of the 2 nd stage, the refrigeration load, and the
temperature distribution in the recuperator are solved using a process similar to that described in
the 1 st stage analysis. The solution process is nearly the same as that of the single stage MGJT
cycle presented in [0]. The only difference is that here, the high pressure gas mixture is
precooled before entering the recuperator, whereas in the single stage system the high pressure
gas mixture enters the recuperator near ambient temperature.
− is iteratively adjusted to achieve a
The recuperator hot end temperature difference ( T T )
4 7
specified recuperator pinch point temperature difference (∆Tpp,rec). The load temperature (T7) is
specified and isenthalpic expansion is assumed across the expansion valve. A numerical model
of the recuperator was created by dividing it into sections of equal heat transfer to calculate an
enthalpy distribution. The enthalpies at states 1, 4, 5, and 7 are used as boundary conditions for
the numerical recuperator model. The enthalpy distribution and recuperator pressures (Ph,2nd and
Pl,2nd) are used to calculate a temperature distribution that facilitates the calculation of mixture
heat capacities and recuperator conductance (UArec).
Overall Thermodynamic Analysis – figures of Merit. The overall system performance can be
quantified using several figures of merit of importance to a MGJT system. From a heat
exchanger size standpoint, an optimal MGJT system is small and generates a large amount of
cooling power. Therefore an appropriate figure of merit [0] that is used to optimize the system is
the total cooling load provided per total heat exchanger conductance, which is indicative of the
heat exchanger size.
Q� load UAtotal = ( Q� load m� nd
2 ) ( UArec m� nd + UA nd
2 pc m�
2 )
(24)
It is also of interest to reduce the size of the other hardware required; particularly the
compressors. The compressors can be connected to the heat exchangers via flexible tubing and
physically decoupled from the precooling and recuperative heat exchangers. Therefore, the size
of the compressors is less important than the size of these heat exchangers. However, the size of
the compressors largely dictates the size and weight of the enclosure that houses the
compressors, as well as the 2 nd stage aftercooler, and 1 st stage condenser. Smaller compressors
will therefore lead to a small system that can more readily be integrated with flight payloads.
The compressor suction side flow rate determines the required displaced volume and therefore,
to first order, the size of the compressor. The figure of merit that captures the combined
compressor size is the refrigeration load per unit of total compressor displacement:
34